Generally, the automotive vehicle is driven by a single internal combustion engine, and the cylinder volume of the internal combustion engine is constant during operation. Since low specific fuel consumption of the internal combustion engine is limited within a small range which is decided by engine torque and engine speed, and since the engine for automotive vehicles is operated under wide driving conditions, the fuel consumption characteristics is aggravated. In order to remove such disadvantages, there is provided an internal combustion engine comprising a plurality of engine units, which are incorporated in accordance with driving conditions of the vehicle for effectively generating a power, whereby fuel consumption characteristic may be improved. For example, Japanese patent publication No. 42-26050 discloses an internal combustion engine, in which a pair of engine units are disposed in parallel and powers of both units are transmitted to an output shaft. Each engine unit is controlled in accordance with load on the engine. However, the publication does not disclose a cooling system for such an engine.